Probabilistic Analysis Method Of Thermos-mechanical Coupling For Functional Gradient Materials Based On Image Processing

Functionally graded materials(FGMs)are advanced composite materials with excellent properties of high temperature resistance and reduce thermal stress,and material compositions varying continuously as a function of spatial position.By varying the relative volume fraction and distribution of the material,functional gradient materials have the performance of continuous spatial variation of material properties.The excellent material properties and designability make functional gradient materials have important applications in the fields of thermal barrier coatings,thermal structures and thermal protection systems for hypercapable vehicles.However,it is difficult to accurately describe the distribution of its heterogeneous components with spatial variation,leading to a biased assessment of the overall macroscopic performance of the structure.Meanwhile,it is always a great challenge for engineering design and reliability assessment for FGMs since there are numerous uncertainties in the manufacturing process,such as the uncertainty of physical parameters,geometric parameters and loads of materials,which result in a strong randomness in the thermal response of the hightemperature structure.According to the above problems,in order to meet the engineering and research needs,this paper starts from the microstructure images of functional gradient materials and uses image segmentation techniques to segment the components of the microstructure of materials to accurately characterize the spatial distribution of materials.And a parametric finite element model of functional gradient material uncertainty is established based on the self-consistent mean micromechanics(Wakashima-Tsukamoto,W-T)model,and a probabilistic analysis method for thermos-mechanical coupling of functional gradient plates considering multiple uncertainty factors is proposed.Meanwhile,a Kriging surrogate model is constructed for the prediction of thermal response by taking random parameters considering the physical properties of the material,spatial distribution and thermal load uncertainty as inputs to the probabilistic analysis,and temperature and thermal stress as outputs.The Kriging model is optimized by introducing the Proper Orthogonal Decomposition(POD)method,which reduces the computational effort of constructing the Kriging model and improves the prediction accuracy for time-history multi-output problems.Finally,a sensitivity analysis of each uncertainty parameter was performed to investigate the effect of random variables on the thermal response.The image segmentation results show that the interactive segmentation method can effectively segment the microstructure images of functional gradient materials.Based on the segmentation results,curve fitting can be used to describe the true distribution of the material components,thus providing a basis for assessing the macroscopic properties of the material.Therefore,this paper provides an accurate and effective method to characterize the component distribution of functional gradient materials by analyzing the microstructure of functional gradient materials through image segmentation technique.The probabilistic analysis method proposed in this paper can efficiently investigate the effects of multiple uncertainty parameters on the thermos-mechanical coupling of functional gradient materials.Numerical examples show that the Kriging surrogate model with uncertainty parameters as input and thermal response as output can predict the maximum temperature and maximum thermal stress of the functional gradient material well;the Kriging model with reduced order of POD has the advantages of small computation and high prediction accuracy in predicting the thermal stress problem on the time history.The results of the sensitivity analysis of each stochastic parameter show that: the spatial distribution power index and the thermal conductivity uncertainty of the ceramic material have a significant effect on the temperature of the structure;the uncertainty variables that have the greatest effect on the maximum thermal stress of the structure are,in order,the thermal conductivity and thermal expansion coefficient of the ceramic,the thermal expansion coefficient of the metal,the modulus of elasticity of the ceramic,and the spatial distribution power index;the thermal load uncertainty has the most significant effect on the temperature and thermal stress response compared to the material properties and the spatial distribution;the thermal load uncertainty makes the maximum temperature and the maximum thermal stress of the structure significantly larger,and also increases the dispersion of the temperature and thermal stress response.